Interestingly, our extended model offers cooperator strategy to survive for smaller synergy factor values which cannot be observed in the traditional model where only public goods game is considered. For a fair competition of attitudes represented by different games, we applied scaled, or weighted values for public goods game to ensure comparable incomes for both games. Interestingly, our qualitative observations remain intact when we apply the original unweighted payoff values of the public goods game. In the latter case the only difference is the parameter range where the 4-state solution emerges moves toward smaller \(r\)  values and evidently the size of the coexistence phase shrinks significantly. For example for \(T=1.02\)  this interval is between \(2.16<r<2.28\) . In sum, our observations fit nicely into previous research experiences which highlight that multi-state spatial population offer novel system behaviors that cannot be detected in well-mixed or unstructured systems and new kind of solutions emerge which would not exist otherwise [1]}, [2]}, [3]}, [4]}, [5]}, [6]}.
